Which guitar to buy for recording purpose?

The frequency of usually encountered radio waves is FAR above what human can ever hope to hear!
For a radio wave about 10000 Hz frequency = about 30 km wavelength!!!

These are very low to ultra low radio frequencies - and require special mammoth sized antennas to detect the signal.

In case the resonant frequency of the antenna alone (λ/4 or λ/2) is different, you may achieve resonance by inductance and capacitance coupling. Which means added inductors and capacitors.

Now a guitar pick-up IS an inductor, so yes, it is possible that the combined inductance of the pickup and the effective length of the conductor (not the actual coil length) couple and produce a resonance that catches the audible part of the EM noise.

(Loading coil - Wikipedia, the free encyclopedia)
(https://en.wikipedia.org/wiki/Loop_antenna)




ACTUALLY, to be simple: a pickup IS an antenna.
Usual radio antenna are designed to pick the electrical field of the EM waves ... the pickup coils are designed to pick the magnetic field of the EM wave.

The fact is that a single coil, humbucker, low output, high output pickups ALL pick up the audible EM signals. Whether these EM signals are due to strings vibrating or due to noise. The only difference is the resonant frequencies of a particular pickup.




Anyway, the next part, why won't you use such low noise guitars in live settings?
You said, because it is more difficult to cause feedback.
But then when you amplify a low output pickup, you are already bringing the signal close to what you would achieve via high output pickup.

Once again numbers:
Low output pikcup = 1 Volt
High output pickup = 2 volt

With low output guitar, you would use gain = 10, whereas for high output guitar you would use gain = 5.
End result - similar overdrive, similar companding of the signal, similar loudness levels.
Hence, similar ease of feedback.

Or perhaps, you want to play with gain 11 when using a low output pickup (but there is no 11 setting available).
In the pedal board populated with hundreds of pedals, there will be at least one tube-screamer clone which you use as a boost pedal ...
So the objective is achieved again.

 

I don't think the mechanical/audio signal frequency matters for the noise that is induced... The carrier signal is an EM/light wave with frequency ranges from 500 kHz (low end AM radio) to 108 MHz (high end of FM). I guess VHF and UHF TV signals go much higher.

I remember how I could hear faint AM radio on my amp when using a bad cable plugged into my distortion box with the gain on max...

 

You mean your amp was acting like a radio receiver?
It picked up the AM - medium wave (cannot demodulate FM unless it was designed for it) at say 1000 kHz.
Demodulated it by separating the carrier frequency at 1000 kHz and reproduced the audible signal (till 9kHz).

Yes, that can also happen - the unshielded and unbalanced cable (guitar to amp) acts like an antenna, and pickups act like inductor.
Thus creating a resonant circuit for the radio waves.
The amp will act like a demod circuit by filtering our the carrier wave, and leaving the "audio signal" pass through.

But this will happen with all the pickups.
There is no reason why it will selectively happen only with the high output pickups.
The problem is with the cables, not pickups.